The authorisation at the request of Obama is scheduled to put to vote early next week.
Soon thereafter the Senate Majority Leader, Harry Reid, hoped to have the necessary 60 votes to get the resolution passed.
The resolution comes to the Senate after the Senate Foreign Relations Committee early this week voted (17-10) for the authorisations.
"I think we are going to have 60 votes. It's a work in progress," Reid told reporters after the resolution was introduced on the Senate floor.
More From This Section
The House of Representatives, in which the opposition Republican party has the majority, is also expected to take a similar vote next week.
"We have another important briefing today. Members have been coming back. I talked to one member just now - he said 'I've been to three briefings.' Have you learned anything? He said, 'I've learned something new on every occasion," Reid said.
Meanwhile, US Secretary of State John Kerry in an opinion piece urged lawmakers to authorise Obama for taking military action, which he said is essential to hold the Bashar al-Assad regime accountable for the use of chemical weapons against civilians.